To determine the time at which all four bells will ring together again, we need to follow these steps carefully:
1. Understanding the Intervals:
We have four bells with ringing intervals of 6, 8, 10, and 15 minutes, respectively.
2. Finding the Least Common Multiple (LCM):
To find the next time all bells ring together, we must determine the smallest time interval that is a multiple of 6, 8, 10, and 15. This interval will be the least common multiple (LCM) of these four numbers.
3. Calculating the LCM:
- The LCM of a set of numbers is the smallest number that all of the given numbers divide into without leaving a remainder.
- The LCM of 6, 8, 10, and 15 has been calculated as 120 minutes.
4. Conversion to Hours and Minutes:
- Convert the time interval (120 minutes) into hours and minutes.
- 120 minutes is equivalent to 2 hours (since 120 divided by 60 equals 2 with a remainder of 0 minutes).
5. Determining the Time:
- We add 2 hours to the initial ring time (8:00 am).
By adding 2 hours to 8:00 am, we get:
8:00 am + 2 hours = 10:00 am
So, the four bells will ring together again at 10:00 am.
